Section 2-3 Histograms. Key Concept We use a visual tool called a histogram to analyze the shape of...

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Section 2-3 Histograms

Transcript of Section 2-3 Histograms. Key Concept We use a visual tool called a histogram to analyze the shape of...

Page 1: Section 2-3 Histograms. Key Concept We use a visual tool called a histogram to analyze the shape of the distribution of the data.

Section 2-3 Histograms

Page 2: Section 2-3 Histograms. Key Concept We use a visual tool called a histogram to analyze the shape of the distribution of the data.

Key Concept

We use a visual tool called a histogram to analyze the shape of the distribution of the data.

Page 3: Section 2-3 Histograms. Key Concept We use a visual tool called a histogram to analyze the shape of the distribution of the data.

Histogram

A graph consisting of bars of equal width drawn adjacent to each other (without gaps). The horizontal scale represents the classes of quantitative data values and the vertical scale represents the frequencies. The heights of the bars correspond to the frequency values.

Page 4: Section 2-3 Histograms. Key Concept We use a visual tool called a histogram to analyze the shape of the distribution of the data.

HistogramBasically a graphic version of a frequency distribution.

Page 5: Section 2-3 Histograms. Key Concept We use a visual tool called a histogram to analyze the shape of the distribution of the data.

HistogramThe bars on the horizontal scale are labeled with one of the following:

(1) Class boundaries

(2) Class midpoints

(3) Lower class limits (introduces a small error)

Horizontal Scale for Histogram: Use class boundaries or class midpoints.

Vertical Scale for Histogram: Use the class frequencies.

Page 6: Section 2-3 Histograms. Key Concept We use a visual tool called a histogram to analyze the shape of the distribution of the data.

Relative Frequency Histogram Has the same shape and horizontal scale as a histogram, but the vertical scale is marked with relative frequencies instead of actual frequencies.

Page 7: Section 2-3 Histograms. Key Concept We use a visual tool called a histogram to analyze the shape of the distribution of the data.

Objective is not simply to construct a histogram, but rather to understand something about the data.

When graphed, a normal distribution has a “bell” shape. Characteristic of the bell shape are

Critical ThinkingInterpreting Histograms

(1) The frequencies increase to a maximum, and then decrease, and

(2) symmetry, with the left half of the graph roughly a mirror image of the right half.

The histogram on the next slide illustrates this.

Page 8: Section 2-3 Histograms. Key Concept We use a visual tool called a histogram to analyze the shape of the distribution of the data.

Critical ThinkingInterpreting Histograms

Page 9: Section 2-3 Histograms. Key Concept We use a visual tool called a histogram to analyze the shape of the distribution of the data.

Critical ThinkingInterpreting Histograms

Example 1: What is the class width? What are the approximate lower and upper class limits of the first class?

Bell shape:

Page 10: Section 2-3 Histograms. Key Concept We use a visual tool called a histogram to analyze the shape of the distribution of the data.

Example 2: The histogram below represents the number of television sets per household for a sample of U.S. households. How many households are included in the histogram?

Page 11: Section 2-3 Histograms. Key Concept We use a visual tool called a histogram to analyze the shape of the distribution of the data.

Example 3: The histogram below represents the number of television sets per household for a sample of U.S. households. How many households have 4 televisions?

Page 12: Section 2-3 Histograms. Key Concept We use a visual tool called a histogram to analyze the shape of the distribution of the data.

Example 4: The histogram below represents the number of television sets per household for a sample of U.S. households. What is the maximum number of households that have the same number of television sets?

Page 13: Section 2-3 Histograms. Key Concept We use a visual tool called a histogram to analyze the shape of the distribution of the data.

Example 5: In a survey, 20 people were asked how many magazines they had purchased during the previous year. The results are shown below. Construct a histogram to represent the data. Use 4 classes, with a class width of 10,and begin with a lower class limit of –0.5. Does the distribution appear to be normal?

6 15 3 36 25 18 12 18 5 3024 7 0 22 33 24 19 4 12 9

Page 14: Section 2-3 Histograms. Key Concept We use a visual tool called a histogram to analyze the shape of the distribution of the data.

Press the STAT button.Choose “1. Edit”

Enter your data in L1 Press “2nd Y=”(STAT PLOT)

Choose “1: Plot 1…”Make your screen look like this:

(turn it ON and choose histogram)Press “Zoom”

Choose “9:ZoomStat”Press “Trace” and use the arrow buttons to move the cursor around your Histogram to determine class widths and frequencies.

Histograms on the Calculator